To solve for [tex]\( F \)[/tex] in the equation [tex]\( C = \frac{5}{9}(F - 32) \)[/tex], let's follow these steps:
1. Understand the equation:
- The given equation relates the temperature in Celsius ([tex]\( C \)[/tex]) to the temperature in Fahrenheit ([tex]\( F \)[/tex]).
2. Identify what we need to do:
- We need to express [tex]\( F \)[/tex] in terms of [tex]\( C \)[/tex].
3. Isolate [tex]\( F \)[/tex]:
- Start with the equation:
[tex]\[
C = \frac{5}{9}(F - 32)
\][/tex]
- Multiply both sides by 9 to clear the fraction:
[tex]\[
9C = 5(F - 32)
\][/tex]
- Divide both sides by 5 to solve for [tex]\( F \)[/tex]:
[tex]\[
\frac{9C}{5} = F - 32
\][/tex]
- Add 32 to both sides to isolate [tex]\( F \)[/tex]:
[tex]\[
F = \frac{9C}{5} + 32
\][/tex]
4. Simplify the equation:
- Noticing that [tex]\(\frac{9}{5}\)[/tex] is equivalent to 1.8 in decimal form, the equation can be written as:
[tex]\[
F = 1.8C + 32.0
\][/tex]
So, the solution to the problem is:
[tex]\[ F = 1.8C + 32.0 \][/tex]
This reveals the temperature conversion formula from Celsius to Fahrenheit.
